Journal of Data Science

In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new models as well as contains two new families as special cases. We explore four special models for the new family. Some mathematical properties of the new family including quantile function, ordinary and incomplete moments, probability weighted moments, Rѐnyi entropy and order statistics are derived. The estimation of the model parameters is performed via maximum likelihood method. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.

In this paper, we introduce a new family of continuous distributions called the transmuted Topp-Leone G family which extends the transmuted class pioneered by Shaw and Buckley (2007). Some of its mathematical properties including probability weighted moments, mo- ments, generating functions, order statistics, incomplete moments, mean deviations, stress- strength model, moment of residual and reversed residual life are studied. Some useful char- acterizations results based on two truncated moments as well as based on hazard function are presented. The maximum likelihood method is used to estimate its parameters. The Monte Carlo simulation is used for assessing the performance of the maximum likelihood estimators. The usefulness of the new model is illustrated by means of two real data set.

Abstract: This paper develops a generalized least squares (GLS) estimator in a linear regression model with serially correlated errors. In particular, the asymptotic optimality of the proposed estimator is established. To obtain this result, we use the modified Cholesky decomposition to estimate the inverse of the error covariance matrix based on the ordinary least squares (OLS) residuals. The resulting matrix estimator maintains positive definite ness and converges to the corresponding population matrix at a suitable rate. The outstanding finite sample performance of the proposed GLS estimator is illustrated using simulation studies and two real datasets.

In this paper, parameter estimation for the power Lomax distribution is studied with different methods as maximum likelihood, maximum product spacing, ordinary least squares, weighted least squares, Cramér–von Mises and Bayesian estimation by Markov chain Monte Carlo (MCMC). Robust estimation of the stress-strength model for the Power Lomax distribution is discussed. We propose that the method of maximum product of spacing for reliable estimation of stress-strength model as an alternative method to maximum likelihood and Bayesian estimation methods. A numerical study using real data and Monte Carlo Simulation is performed to compare between different methods.

Abstract: Constrained general linear models (CGLMs) have wide applications in practice. Similar to other data analysis, the identification of influential obser vations that may be potential outliers is an important step beyond in CGLMs. We develop local influence approach for detecting influential observations in CGLMs. The procedure makes use of the normal curvature and the direction achieving the maximum curvature to assess the local influences of minor perturbation of CGLMs. An illustrative example with a real data set is also reported.

Abstract: We group approaches to modeling correlated binary data accord ing to data recorded cross-sectionally as opposed to data recorded longi tudinally; according to models that are population-averaged as opposed to subject-specific; and according to data with time-dependent covariates as opposed to time-independent covariates. Standard logistic regression mod els are appropriate for cross-sectional data. However, for longitudinal data, methods such as generalized estimating equations (GEE) and generalized method of moments (GMM) are commonly used to fit population-averaged models, while random-effects models such as generalized linear mixed mod els (GLMM) are used to fit subject-specific models. Some of these methods account for time-dependence in covariates while others do not. This paper addressed these approaches with an illustration using a Medicare dataset as it relates to rehospitalization. In particular, we compared results from standard logistic models, GEE models, GMM models, and random-effects models by analyzing a binary outcome for four successive hospitalizations. We found that these procedures address differently the correlation among responses and the feedback from response to covariate. We found marginal GMM logistic regression models to be more appropriate when covariates are classified as time-dependent in comparison to GEE models. We also found conditional random-intercept models with time-dependent covariates decom posed into components to be more appropriate when time-dependent covari ates are present in comparison to ordinary random-effects models. We used the SAS procedures GLIMMIX, NLMIXED, IML, GENMOD, and LOGIS TIC to analyze the illustrative dataset, as well as unique programs written using the R language.

Abstract: A powerful methodology for exploring relationships among items, association rules analysis can be used to capture a set of rules from any given dataset. Little is known, however, that a single dataset can be represented by more than one set of rules, i.e., by equivalent models. In fact, most studies on the goodness of model can be misleading because they assume the model is unique. These are phenomenon that the literature has yet to explore. In our study, we demonstrate that equivalent models exist for any dataset and propose a method for converting any given model into its dominant model, recommended as the benchmark model. Further, we explain how the phenomenon of equivalent models affects decision tree analysis and statistical model selection. It is shown that the decision rules from decision tree analysis can always be simplified by reducing the decision rules to the dominant model. The simulated and real datasets are used for illustration.

Abstract: In recent years, many modifications of the Weibull distribution have been proposed. Some of these modifications have a large number of parameters and so their real benefits over simpler modifications are questionable. Here, we use two data sets with modified unimodal (unimodal followed by increasing) hazard function for comparing the exponentiated Weibull and generalized modified Weibull distributions. We find no evidence that the generalized modified Weibull distribution can provide a better fit than the exponentiated Weibull distribution for data sets exhibiting the modified unimodal hazard function.In a related issue, we consider Carrasco et al. (2008), a widely cited paper, proposing the generalized modified Weibull distribution, and illustrating two real data applications. We point out that some of the results in both real data applications in Carrasco et al. (2008) 1 are incorrect.

An exponentiated Weibull-geometric distribution is defined and studied. A new count data regression model, based on the exponentiated Weibull-geometric distribution, is also defined. The regression model can be applied to fit an underdispersed or an over-dispersed count data. The exponentiated Weibull-geometric regression model is fitted to two numerical data sets. The new model provided a better fit than the fit from its competitors.

Abstract: Bivariate data analysis plays a key role in several areas where the variables of interest are obtained in a paired form, leading to the con sideration of possible association measures between them. In most cases, it is common to use known statistics measures such as Pearson correlation, Kendall’s and Spearman’s coefficients. However, these statistics measures may not represent the real correlation or structure of dependence between the variables. Fisher and Switzer (1985) proposed a rank-based graphical tool, the so called chi-plot, which, in conjunction with its Monte Carlo based confidence interval can help detect the presence of association in a random sample from a continuous bivariate distribution. In this article we construct the asymptotic confidence interval for the chi-plot. Via a Monte Carlo simulation study we discovery the coverage probabilities of the asymptotic and the Monte Carlo based confidence intervals are similar. A immediate advantage of the asymptotic confidence interval over the Monte Carlo based one is that it is computationally less expensive providing choices of any confidence level. Moreover, it can be implemented straightforwardly in the existing statistical softwares. The chi-plot approach is illustrated in on the average intelligence and atheism rates across nations data.